Doesn't look like it worked for you, here's another version to try... it's very high contrast (ugly looking for me):
Try saving that one. Here's what it looks like for me with the Other Outlines OFF:
You should definitely notice the difference with this version if it's working correctly.
Make sure the the file is exactly named "TileSelectionTexture_Tactical.dds", and is definitely sitting in the ..... Documents\My Games\LegendaryHeroes\Mods\Gfx folder.
If that still isn't working then... do you have any other mods installed?
The other thing you could do is to try overwriting the default one in the core folder. It's located in:
... Steam\SteamApps\common\FE Legendary Heroes\Gfx
You'll find a file called "TileSelectionTexture_Tactical.dds" in that location. Rename it to something else (eg. "TileSelectionTexture_Tactical.dds.original" then drop one of my version in there. That should definitely change it... just bear in mind that Steam might overwrite it when it updates the game.
Let me know how that goes.